DETROIT – The Tampa Bay Lightning have a horrible history at Joe Louis Arena.

But, it seems the Joe is the place to be for visiting teams these days.

Teddy Purcell scored with 1:09 left in overtime Saturday as the Lightning defeated the Red Wings 3-2, extending Detroit’s home winless streak to five games (0-1-4).

This is the Red Wings’ longest home winless skid since the end of the 1996-97 season, when they went 0-2-2-1 (W-L-T-OTL). Since winning an NHL record 23-comsecutive home games during the 2011-12 season, the Red Wings are 21-15-9 at JLA.

The streaky Red Wings (9-5-4) are winless in three overall (0-1-2).

Purcell scored on a shot from the slot against Jimmy Howard, following a turnover behind the net by Kyle Quincey.

Henrik Zetterberg scored his second goal of the game, his team-leading 10th of the season, to tie it at 2-2 with 4:12 remaining in the third period.

The Lightning took the lead early in the second period. The Red Wings had four consecutive power plays – a total of 7:24 on the man-advantage, including a five-on-three for 36 seconds – and couldn’t capitalize.

Just four seconds after that stretch of power-play time expired, the Lightning snapped a 1-1 tie on Steven Stamkos’ 14th goal, which tied him with Alexander Steen for the NHL lead.

It was the result of a mix-up at the Detroit blue line. The puck hit Zetterberg’s shin and stayed in the zone. Viktor Hedman passed to a wide-open Stamkos at the edge of the faceoff circle. He blasted it over Howard’s shoulder.

Red Wings coach Mike Babcock joked before the game that he hoped Stamkos wore out his arms from having so many clear-cut chances in the Lightning’s previous game.

“I’m hoping we’re not going to give him quite as much room as that,’’ Babcock said.

They did, and he made them pay.

“Obviously, he’s a gifted player,’’ Babcock said. “He’s a competitive kid. He’s worked hard at his body. It looks to me from watching the last few games that he’s worked hard on his game to be better defensively. But he’s dangerous. He can really skate, he can really shoot it and he loves to score.’’

Said Zetterberg of Stamkos: “He’s one of the best players in the league. If you give him a little bit he takes a lot. He can shoot from everywhere and score from anywhere.’’

The teams traded goals in the first period.

Zetterberg notched his first goal of the game at 3:51, unassisted. It was a shot from the slot following a Stamkos turnover.

Ryan Malone tied it at 10:11, scoring on the second effort during a wraparound, as a defensive breakdown, during a bad change, left that side of the net unguarded.

This was Tampa Bay’s first win in Detroit since Jan. 12, 1994 (4-2). The Red Wings were 13-1-1 all-time vs. Tampa Bay at home (W-L-T). They had gone undefeated in 11 consecutive home games vs. the Lightning (10-0-1 -- W-L-T) before Saturday.